This is the spleenwort fern. It is a fractal generated by the IFS
(Iterated Function System) method. In sum, the above shape is infinitely
complex. No matter what resolution the actual shape is viewed at (this
GIF representation, of course, does not possess infinite resolution), it
will always appear infinitely fine. It can be printed or viewed at any
resolution with no loss of quality.
And the cost of storage of this magnificent shape? All it takes to store
this shape is four 2x2 transformation matrices, four 2x1 translational
matrices, and four scalar probabilities. That, my friends, is a
sum total of twenty-eight numeric values.
It is blindingly simple to construct the spleenwort fern above. Represent
your coordinates as a vertical vector and use the four sets of affine
transformations above. For each iteration, select one of the
transformation sets at random (given the weighted probabilities). Then
multiply your current by the transformation, add the translational vector, and
plot the point. Iterate infinitely. And there you are, in living
Much, much, more will be added as time passes.
Return to Chaos Hompage